Problems of Number Theory in Mathematical Competitions
Number theory is an important research field of mathematics. In mathematical competitions, problems of elementary number theory occur frequently. These problems use little knowledge and have many variations. They are flexible and diverse. In this book, the author introduces some basic concepts and methods in elementary number theory via problems in mathematical competitions. Readers are encouraged to try to solve the problems by themselves before they read the given solutions of examples. Only in this way can they truly appreciate the tricks of problem-solving.
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&-th power Bezout's identity binomial theorem Chapter Chinese remainder theorem choose clearly true completes the proof congruent modulo consecutive integers consecutive positive integers contradiction deduce denote division algorithm Euler's theorem expressed Fermat's little theorem Find all integer finite number following Example gcd(a gcd(xr given condition greatest common divisor Hence implies indeterminate equation induction infinitely many primes integer coefficients k0 satisfies least common multiple left side mathematical competition meet the requirement mod 9 mod n modulo 9 modulo n odd number odd prime divisor original equation pairwise relatively prime perfect square polynomial with integer positive integer solutions positive number power number prime factorization prime number problems of number proof of Example rational number reduced system modulo relatively prime pairwise Remark required numbers result right side Similarly solve standard factorization Suppose system of congruences unique factorization theorem